Abstract <p>The purpose of the work is the development, software implementation, and testing of algorithms designed to find resonant frequencies in an inhomogeneous dielectric ball coated with graphene. The relevance of the task is due to the widespread use of graphene in engineering due to its unique properties. The Galerkin method is applied to discretize a vector integrodifferential equation; piecewise-constant basis vector functions are determined on a three-dimensional body and on its surface, and a parallel algorithm for solving the problem is developed using the MSMPI library. The effectiveness of the parallel algorithm, which makes it possible to detect the sought resonances under specified conditions, has been confirmed. An effective parallel algorithm has been created for discretizing the integrodifferential equation, finding the determinant of the matrix, and searching for resonant frequencies.</p>